Secondary Filament
Robert P. Munafo, 2023 Mar 13.
In the nomenclature developed for the R2 naming system, a secondary filament is a connected set which is a subset of a primary filament and which is one of the "pieces" that remains after the lowestperiod island is removed from that primary filament.
To illustrate by example, consider the "largest" primary filament, which is the one stretching from about 1.5437+0i out to the tip at 2+0i. This filament contains the largest island, R2F(1/2B1)S. If that island is removed, what remains is a lot of pieces that are each themselves connected sets, but are not connected to each other.
The Secondary Filaments of R2F(1/2B1)

Filament Subset Operation
Of all the islands in a secondary filament, there is exactly one with lowest period. If that island is omitted, what remain are an infinite set of "tertiary" filaments. The filament subset operator (see R2 rules) gives names to the tertiary filaments, and it can be applied repeatedly to generate names for "quaternary", etc. filaments.
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 19872024.
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